Methane gas (CH4) effuses 3.4 times faster than an unknown gas. Determine the molar mass of the unknown gas. Show your work or explain your answer, giving specific values used to determine the answer.

184.96 g/mol

Explanation:

Let R1 be the rate of effusion of the unknown gas

Let R2 be the rate of effusion of CH4

The following data were obtained from the question:

Let the Rate of effusion of the unknown gas (R1) = 1

Therefore, the Rate of effusion of CH4 (R2) = 3.4 times R1 = 3.4 × 1 = 3.4

Molar mass (M2) of CH4 = 12 + (1×4) = 12 + 4 = 16 g/mol

Molar mass (M1) of the unknown gas =?

Thus, we can obtain the molar mass of the unknown gas as shown below:

R1/R2 = √(M2/M1)

1/3.4 = √(16/M1)

Take the square of both side

(1/3.4)² = 16/M1

1/11.56 = 16/M1

Cross multiply

1 × M1 = 11.56 × 16

M1 = 184.96 g/mol

Therefore, the molar mass of the unknown gas is 184.96 g/mol

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